312 



GRAPHICAL METHODS. 



Art. 157 



157. Graphical Methods. 1 For finding the position 

 of the loads for maximum moments and shears, the graphical 

 method is elegant, rapid and accurate. The application of the 

 criteria are nearly always made graphically. The stresses are 

 usually calculated from the actual wheel loads by the use of 

 moment tables. We shall consid3r the special case of a truss 

 in which the top chord joints are vertically over those of the 

 bottom chord. Fig. 209 is a diagram of Cooper's class #40 Load- 

 ing (see Fig. 19S), laid out so that the ordinate at any point is 

 equal to the sum of the loads to the left of that point, that is, the 

 heights of the steps are equal to the wheel loads by scale. 



To find the position of the loads for maximum moment at D 

 we use equation (84), which requires that the load per foot on the 

 whole span be equal to the load per foot to the left of D. Now 

 the load on the span is represented by FH EG and on AD by 

 NMEG or NKEG, depending on whether load 11 is counted 

 with the load on AD or DB. We must have then, if a maximum 

 moment occurs when wheel 11 is at D, 



NKEG FIIEG 

 -> 



AD 



AB 



, NMEG HI EG 

 and --AlT-<- 



1 For a more extended discussion of graphical methods, see Johnson's 

 Modern Framed Structures," Ninth edition, Part I, page 218, 



